Division with Mixed Index and Power of Radicand (Fraction) - Integer over Radical (Level 2)

This math topic focuses on simplifying radical expressions, specifically handling division problems involving mixed indices and powers of the radicand. It involves simplifying radicals where an integer is divided by a radical expression, which may also be to a fractional power. The exercises are designed to challenge understanding of simplifying radical expressions as part of a broader unit on radicals. Each problem provides multiple-choice answers, emphasizing the application of radical rules and properties for correct simplification.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

more
View

Radicals - Division with Mixed Index and Power of Radicand (Fraction) - Integer over Radical Worksheet

Mobius Math Academy logo
Radicals - Division with Mixed Index and Power of Radicand (Fraction) - Integer over Radical
1
What does this radical expression simplify to?
A LaTex expression showing 216 over 3-th root of 64 to the power of 3
a A LaTex expression showing 13 over 40
b A LaTex expression showing 27 over 8
c A LaTex expression showing 167 over 113
d A LaTex expression showing 174 over 113
e A LaTex expression showing 120 over 61
2
What does this radical expression simplify to?
A LaTex expression showing 16 over 3-th root of 49 to the power of 3
a A LaTex expression showing 16 over 49
b A LaTex expression showing 29 over 65
c A LaTex expression showing 27 over 28
d A LaTex expression showing 17 over 24
e A LaTex expression showing 9 over 68
3
What does this radical expression simplify to?
A LaTex expression showing 9 over 2-th root of 27 to the power of 2
a A LaTex expression showing 8 over 35
b A LaTex expression showing 7 over 26
c A LaTex expression showing 1 over 20
d A LaTex expression showing 16 over 41
e A LaTex expression showing 1 over 3
4
What does this radical expression simplify to?
A LaTex expression showing 216 over 3-th root of 27 to the power of 4
a A LaTex expression showing 40 over 41
b A LaTex expression showing 118 over 75
c A LaTex expression showing 13
d A LaTex expression showing 8 over 3
e A LaTex expression showing 74 over 65
5
What does this radical expression simplify to?
A LaTex expression showing 4 over 2-th root of 4 to the power of 5
a A LaTex expression showing 3 over 5
b A LaTex expression showing 3 over 8
c A LaTex expression showing 1 over 8
d A LaTex expression showing 2 over 23
e A LaTex expression showing 1 over 12
6
What does this radical expression simplify to?
A LaTex expression showing 27 over 3-th root of 9 to the power of 3
a A LaTex expression showing 6 over 5
b A LaTex expression showing 15 over 8
c A LaTex expression showing 9 over 5
d A LaTex expression showing 25 over 13
e A LaTex expression showing 3
7
What does this radical expression simplify to?
A LaTex expression showing 32 over 3-th root of 16 to the power of 3
a A LaTex expression showing 13
b A LaTex expression showing 9 over 4
c A LaTex expression showing 35 over 34
d A LaTex expression showing 2
e A LaTex expression showing 6 over 7
8
What does this radical expression simplify to?
A LaTex expression showing 36 over 2-th root of 4 to the power of 4
a A LaTex expression showing 49 over 32
b A LaTex expression showing 17 over 19
c A LaTex expression showing 3 over 4
d A LaTex expression showing 32 over 27
e A LaTex expression showing 9 over 4